This work evaluates the friction coefficient using the model of plastic hemispherical contact against a rigid flat. The fractional profile of an ellipsoid is utilized to describe the deformed hemispherical shape, and simultaneously define the contact area ratio. Particularly, an adhesion factor is defined to assess the junction ability of asperity adhesion under compressive loading. Additionally, the complex process of contact is assumed as a series of contact states changing from fracture to shearing. The friction coefficient, which obeys the constant friction law, is then derived as a function of interference and strain hardening exponent via adhesion theory. Finally, a comparison of friction coefficient is made with the published experiment, showing that the calculated value is larger than the experimental value. Some practical conclusions are presented and a conceptual understanding of contact friction is provided.